A student struggles to identify a pair of positive integers, given their sum as well as the
sum of their greatest common factor and least common multiple. Doctor Greenie
applies some algebra and factorization to turn the problem into a Diophantine
equation.

As I read various algebra books for high school kids, I find what
appears to be an inconsistent use of the words 'quadratic equation',
and I wanted to be sure I use it correctly myself. Is it correct to
call y = ax^2 + bx + c a 'quadratic equation', or a 'quadratic function'?

Given three points, two with unknown abscissas, a student has doubts about their
collinearity. After offering some leading hints, Doctor Mike invokes the point-slope
form to rigorously confirm the student's suspicions.